Incentivizing Agents through Ratings (2407.10525v4)

Abstract: I study the optimal design of ratings to motivate agent investment in quality when transfers are unavailable. The principal designs a rating scheme that maps the agent's quality to a (possibly stochastic) score. The agent has private information about his ability, which determines his cost of investment, and chooses the quality level. The market observes the score and offers a wage equal to the agent's expected quality. For example, a school incentivizes learning through a grading policy that discloses the student's quality to the job market. I reduce the principal's problem to the design of an interim wage function of quality. When restricted to deterministic ratings, I provide necessary and sufficient conditions for the optimality of simple pass/fail tests and lower censorship. In particular, when the principal's objective is expected quality, pass/fail tests are optimal if agents' abilities are concentrated towards the top of the distribution, while pass/lower censorship is optimal if abilities are concentrated towards the mode. The results generalize existing results in optimal delegation with voluntary participation, as pass/fail tests (lower censorship) correspond to take-it-or-leave-it offers (threshold delegation). Additionally, I provide sufficient conditions for deterministic ratings to remain optimal when stochastic ratings are allowed. For quality maximization, pass/fail tests remain optimal if the ability distribution becomes increasingly more concentrated towards the top.